1.\" Copyright (c) 1985, 1991 Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 3. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.Dd March 10, 2015 29.Dt J0 3 30.Os 31.Sh NAME 32.Nm j0 , 33.Nm j0f , 34.Nm j1 , 35.Nm j1f , 36.Nm jn , 37.Nm jnf , 38.Nm y0 , 39.Nm y0f , 40.Nm y1 , 41.Nm y1f , 42.Nm yn , 43.Nm ynf 44.Nd Bessel functions of first and second kind 45.Sh LIBRARY 46.Lb libm 47.Sh SYNOPSIS 48.In math.h 49.Ft double 50.Fn j0 "double x" 51.Ft float 52.Fn j0f "float x" 53.Ft double 54.Fn j1 "double x" 55.Ft float 56.Fn j1f "float x" 57.Ft double 58.Fn jn "int n" "double x" 59.Ft float 60.Fn jnf "int n" "float x" 61.Ft double 62.Fn y0 "double x" 63.Ft float 64.Fn y0f "float x" 65.Ft double 66.Fn y1 "double x" 67.Ft float 68.Fn y1f "float x" 69.Ft double 70.Fn yn "int n" "double x" 71.Ft float 72.Fn ynf "int n" "float x" 73.Sh DESCRIPTION 74The functions 75.Fn j0 , 76.Fn j0f , 77.Fn j1 , 78and 79.Fn j1f 80compute the Bessel function of the first kind of orders 810 and 1 for the real value 82.Fa x ; 83the functions 84.Fn jn 85and 86.Fn jnf 87compute the Bessel function of the first kind of the integer order 88.Fa n 89for the real value 90.Fa x . 91.Pp 92The functions 93.Fn y0 , 94.Fn y0f , 95.Fn y1 , 96and 97.Fn y1f 98compute the linearly independent Bessel function of the second kind 99of orders 0 and 1 for the positive 100.Em real 101value 102.Fa x ; 103the functions 104.Fn yn 105and 106.Fn ynf 107compute the Bessel function of the second kind for the integer order 108.Fa n 109for the positive 110.Em real 111value 112.Fa x . 113.Sh RETURN VALUES 114These routines return values of their respective Bessel functions. 115For large positive inputs, they may underflow and return \*(Pm0. 116.Pp 117The following applies to 118.Fn y0 , 119.Fn y0f , 120.Fn y1 , 121.Fn y1f , 122.Fn yn , 123and 124.Fn ynf . 125If 126.Fa x 127is negative, including -\*(If, these routines will generate an invalid 128exception and return \*(Na. 129If 130.Fa x 131is \*(Pm0, these routines 132will generate a divide-by-zero exception and return -\*(If. 133If 134.Fa x 135is a sufficiently small positive number, then 136.Fn y1 , 137.Fn y1f , 138.Fn yn , 139and 140.Fn ynf 141will generate an overflow exception and return -\*(If. 142.Sh SEE ALSO 143.Xr math 3 144.Sh STANDARDS 145The 146.Fn j0 , 147.Fn j1 , 148.Fn jn , 149.Fn y0 , 150.Fn y1 , 151and 152.Fn yn 153functions conform to 154.St -p1003.1-2001 . 155The 156.Ft float 157versions are extensions. 158.Sh HISTORY 159This set of functions 160appeared in 161.At v7 . 162